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Parallel Control for Nonzero-Sum Games With Completely Unknown Nonlinear dynamics via Reinforcement Learning

IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2025年第4期55卷 2884-2896页

作者： Lu, Jingwei Wei, Qinglai Wang, Fei-Yue Tsinghua Univ Dept Ind Engn Beijing 100084 Peoples R China Chinese Acad Sci Inst Automat State Key Lab Multimodal Artificial Intelligence S Beijing 100190 Peoples R China Macau Univ Sci & Technol Inst Syst Engn Macau Peoples R China Chinese Acad Sci Inst Automat State Key Lab Management & Control Complex Syst Beijing 100190 Peoples R China Macau Univ Sci & Technol Fac Innovat Engn Macau Peoples R China

This article utilizes parallel control to investigate the problem of continuous-time (CT) nonzero-sum games (NZSGs) for completely unknown nonlinear systems via reinforcement learning (RL), and a parallel control-based NZSG (PNZSG) method is developed without reconstructing unknown dynamics or employing off-policy integral RL (IRL). First, novel dynamic control policies (DCPs) are developed for NZSGs by introducing controls into feedback, and an augmented system with augmented performance indices is constructed to derive the DCPs. Then, we theoretically analyze the effect of the DCPs on the control stability and performance indices, and the optimality of PNZSG is proven to be equivalent to the optimality of the original NZSGs. Subsequently, an IRL technique is employed to achieve the developed PNZSG method, and we show that no prior knowledge of the dynamics of NZSGs is needed to deploy the developed PNZSG method because of the augmented system and performance indices. Finally, numerical examples, including cooperative adaptive cruise control (CACC) of a vehicular platoon, demonstrate the correctness of the developed PNZSG method. The associated code is available at: https://***/lujingweihh/adaptive-dynamic-programming-algorithms/tree/main/model_free_nonzero_sum_games.

关键词： adaptive dynamic programming cooperative adaptive cruise control (CACC) cooperative adaptive cruise control (CACC) nonzero-sum games (NZSGs) nonzero-sum games (NZSGs) parallel control parallel control reinforcement learning (RL) reinforcement learning (RL) unknown nonlinear dynamics unknown nonlinear dynamics unknown nonlinear dynamics unknown nonlinear dynamics unknown nonlinear dynamics

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Data-Driven dynamic Output Feedback Nash Strategy for Multi-Player Non-Zero-Sum Games

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Journal of Systems Science & Complexity 2025年第2期38卷 597-612页

作者： XIE Kedi LU Maobin DENG Fang SUN Jian CHEN Jie School of Automation Beijing Institute of Technology Beijing Institute of Technology Chongqing Innovation Center Harbin Institute of Technology

This paper investigates the multi-player non-zero-sum game problem for unknown linear continuous-time systems with unmeasurable states. By only accessing the data information of input and output, a data-driven learning control approach is proposed to estimate N-tuple dynamic output feedback control policies which can form Nash equilibrium solution to the multi-player non-zero-sum game problem. In particular, the explicit form of dynamic output feedback Nash strategy is constructed by embedding the internal dynamics and solving coupled algebraic Riccati equations. The coupled policy-iteration based iterative learning equations are established to estimate the N-tuple feedback control gains without prior knowledge of system matrices. Finally, an example is used to illustrate the effectiveness of the proposed approach.

关键词： adaptive dynamic programming non-zero-sum games output feedback policy-iteration

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Event-triggered optimal control with finite-time convergence critic networks for input-constrained nonlinear systems

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PHYSICA SCRIPTA 2025年第1期100卷

作者： Liu, Yizhuo Ma, Kemao Harbin Inst Technol Sch Astronaut Harbin 150001 Peoples R China Natl Key Lab Complex Syst Control & Intelligent Ag Harbin 150001 Peoples R China

This paper proposes an adaptive critic design-based event-triggered optimal control method for input-constrained continuous-time nonlinear systems. adaptive critic design is a special framework of adaptive dynamic programming that approximates the value function by a critic neural network and derives the approximate optimal control policy through analytical methods. The proposed adaptive critic design considers the control input constraints by introducing a non-quadratic cost function and employs an event-triggered mechanism to reduce the number of controller executions. Unlike the existing event-triggered adaptive critic design, this paper proposes a novel finite-time adaptive law based on regression filtering scheme. The adaptive law utilizes the error information of the network weights to ensure fast convergence to the optimal control law under the event-triggered mechanism, which improves the real-time performance of the system. Additionally, explicit bounds for each parameter in the compact set and the specific convergence time estimates are provided in the convergence analysis. Finally, the effectiveness and practicality of the proposed method for real-time online applications are validated through two simulation examples.

关键词： adaptive critic design adaptive dynamic programming event-triggered control finite-time convergence input constraints

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Integral Reinforcement Learning-Based dynamic Event-Triggered Nonzero-Sum Games of USVs

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IEEE TRANSACTIONS ON CYBERNETICS 2025年第4期55卷 1706-1716页

作者： Xue, Shan Zhang, Weidong Luo, Biao Liu, Derong Hainan Univ Sch Informat & Commun Engn Haikou 570228 Peoples R China Shanghai Jiao Tong Univ Dept Automat Shanghai 200240 Peoples R China Cent South Univ Sch Automat Changsha 410083 Peoples R China Southern Univ Sci & Technol Sch Automat & Intelligent Mfg Shenzhen 518055 Peoples R China Univ Illinois Dept Elect & Comp Engn Chicago IL 60607 USA

In this article, an integral reinforcement learning (IRL) method is developed for dynamic event-triggered nonzero-sum (NZS) games to achieve the Nash equilibrium of unmanned surface vehicles (USVs) with state and input constraints. Initially, a mapping function is designed to map the state and control of the USV into a safe environment. Subsequently, IRL-based coupled Hamilton-Jacobi equations, which avoid dependence on system dynamics, are derived to solve the Nash equilibrium. To conserve computational resources and reduce network transmission burdens, a static event-triggered control is initially designed, followed by the development of a more flexible dynamic form. Finally, a critic neural network is designed for each player to approximate its value function and control policy. Rigorous proofs are provided for the uniform ultimate boundedness of the state and the weight estimation errors. The effectiveness of the present method is demonstrated through simulation experiments.

关键词： Vehicle dynamics Event detection Games Mathematical models Nash equilibrium Heuristic algorithms Neural networks Electronic mail Computational modeling Reinforcement learning adaptive dynamic programming event-triggered control integral reinforcement learning (IRL) neural network unmanned surface vehicle (USV)

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Concurrent Learning Critic-Only NN-Based Robust Approximate Optimal Control of Nonlinear Systems With Experimental Verification

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 2025年

作者： Zhang, Haichao Wang, Xin Xiao, Bing Wu, Xiwei Li, Bo Northwestern Polytech Univ Sch Automat Xian 710072 Peoples R China China Aerosp Acad Syst Sci & Engn Beijing 100037 Peoples R China Shanghai Maritime Univ Inst Logist Sci & Engn Shanghai 201306 Peoples R China

This article addresses the optimal control problem for a class of continuous-time nonlinear systems with time-varying bounded disturbances. A novel approximate optimal control policy that incorporates a continuous robust control command is developed within the framework of adaptive dynamic programming. It makes the controlled system robust to the bounded time-varying disturbance rather than just the disturbance that vanishes as the system state converges. Moreover, an improved concurrent learning neural network (NN) weight updating algorithm that involves a switching mechanism is presented, and it can work without persistent/finite assumptions. Then, with the uniformly ultimately bounded stability guaranteed by Lyapunov theory, the closed-loop controlled system achieves approximate optimality and strong robustness. The superiority and effectiveness of the suggested control approach have been demonstrated via robotic trajectory tracking experiments.

关键词： Optimal control Nonlinear systems Uncertainty Stability analysis Time-varying systems Cost function Switches Mathematical models Space vehicles Iron adaptive dynamic programming concurrent learning perturbed control system robust approximate optimal control wheeled mobile robot

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ADP-Based Optimal Control for Discrete-Time Systems With Safe Constraints and Disturbances

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2025年 22卷 115-128页

作者： Ye, Jun Dong, Hongyang Bian, Yougang Qin, Hongmao Zhao, Xiaowei Hunan Univ Coll Mech & Vehicle Engn Changsha 410082 Peoples R China Univ Warwick Sch Engn Intelligent Control & Smart Energy ICSE Res Grp Coventry CV4 7AL W Midlands England

In this paper, a novel adaptive dynamic programming (ADP)-based optimal control method is developed for discrete-time systems subject to constraints and disturbances. Particularly, a safe policy iteration scheme is designed to handle state and input constraints, including both hard and soft constraints, by converting the original policy improvement strategy into a constrained optimization problem with a prescribed state cost function. After that, an actor-critic-disturbance framework is introduced to address the constrained optimal control problem. The robust safety against disturbances is treated as a two-player zero-sum game, where the actor and disturbance neural networks are used to approximate the optimal control input and the disturbance policy, respectively. The convergence property of the proposed algorithm is analyzed, and the multi-step version of the proposed ADP scheme is derived based on this property. Simulation results are demonstrated and discussed to validate the effectiveness and performance of the proposed method.

关键词： Optimal control Safety Discrete-time systems Games Cost function Convergence Adaptation models adaptive dynamic programming discrete-time systems optimal control constrained control zero-sum game

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Learning-based tracking control of AUV:Mixed policy improvement and game-based disturbance rejection

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CAAI Transactions on Intelligence Technology 2025年第2期10卷 510-528页

作者： Jun Ye Hongbo Gao Manjiang Hu Yougang Bian Qingjia Cui Xiaohui Qin Rongjun Ding State Key Laboratory of Advanced Design and Manufacturing Technology for Vehicle College of Mechanical and Vehicle EngineeringHunan UniversityChangshaChina School of Information Science and Technology and Institute of Advanced TechnologyUniversity of Science and Technology of ChinaHefeiChina Nanyang Technological University SingaporeSingapore Wuxi Intelligent Control Research Institute of Hunan University Hunan UniversityWuxiChina

A mixed adaptive dynamic programming(ADP)scheme based on zero-sum game theory is developed to address optimal control problems of autonomous underwater vehicle(AUV)systems subject to disturbances and safe *** combining prior dynamic knowledge and actual sampled data,the proposed approach effectively mitigates the defect caused by the inaccurate dynamic model and significantly improves the training speed of the ADP ***,the dataset is enriched with sufficient reference data collected based on a nominal model without considering modelling ***,the control object interacts with the real environment and continuously gathers adequate sampled data in the *** comprehensively leverage the advantages of model-based and model-free methods during training,an adaptive tuning factor is introduced based on the dataset that possesses model-referenced information and conforms to the distribution of the real-world environment,which balances the influence of model-based control law and data-driven policy gradient on the direction of policy *** a result,the proposed approach accelerates the learning speed compared to data-driven methods,concurrently also enhancing the tracking performance in comparison to model-based control ***,the optimal control problem under disturbances is formulated as a zero-sum game,and the actor-critic-disturbance framework is introduced to approximate the optimal control input,cost function,and disturbance policy,***,the convergence property of the proposed algorithm based on the value iteration method is ***,an example of AUV path following based on the improved line-of-sight guidance is presented to demonstrate the effectiveness of the proposed method.

关键词： adaptive dynamic programming autonomous underwater vehicle game theory optimal control reinforcement learning

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Action-dependent heuristic dynamic programming for hybrid-order systems based on dynamic event-triggered mechanism

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NEUROCOMPUTING 2024年 600卷

作者： Li, Jun Li, Huaqing Zheng, Lifeng Ran, Liang Ji, Lianghao Southwest Univ Chongqing Key Lab Nonlinear Circuits & Intelligent Tiansheng St Chongqing 400715 Peoples R China Chongqing Univ Posts & Telecommun Chongqing Key Lab Image Cognit Chongwen Rd Chongqing 400065 Peoples R China

We investigate the distributed optimal consensus control problem based on action-dependent heuristic dynamic programming (ADHDP). In order to strike a stable balance between the learning cost of reinforcement learning and the resource utilization efficiency of the hybrid-order multi-agent systems (MASs), we propose an improved dynamic event-triggered ADHDP (dET-ADHDP) method. This approach can non-periodically explore the control policy distribution using the online action-dependent actor-critic (ADAC) learning framework. Meanwhile, it can dynamically adjust the trigger lower bound by exploiting the designed trigger threshold function, and adaptively decide the signal trigger moment during the ADAC learning process. In addition, we demonstrate the boundedness of the ADAC network weights and show that under the designed dynamic event-triggering rules, the MASs can asymptotically achieve optimal tracking control without Zeno phenomenon. Finally, compared with the traditional static counterparts, simulation experiments demonstrate that the proposed dynamic eventtriggered ADAC (dET-ADAC) algorithm has more efficient resource utilization while maintaining satisfactory learning performance.

关键词： adaptive dynamic programming Optimal consensus control dynamic event-triggered mechanism Heterogeneous multi-agent systems

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Event-triggered-based distributed differential game guidance laws

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART G-JOURNAL OF AEROSPACE ENGINEERING 2024年第16期238卷 1638-1650页

作者： Xi, Axing Cai, Yuanli Xi ?an Jiaotong Univ Sch Automat Sci & Engn Xian Peoples R China

To reduce computational loads and save communication resources of multi-missile systems, event-triggered-based distributed differential game guidance laws for the nonlinear cooperative multi-missile system are investigated. First, the cooperative multi-missile interception problem is converted into multi-player zero-sum differential games, where all missiles minimize the cost function while the target maximizes the cost function. Second, event-triggered conditions are designed, for implementing the proposed guidance laws, adaptive dynamic programming technique is adopted to approximate the couple event-triggered Hamilton-Jacobi-Isaacs equation, and adaptive weight-tuning laws are proposed. Furthermore, the proposed guidance laws can guarantee the stability of the nonlinear multi-missile system, which is proved by Lyapunov theory. The estimated weights of neural network and consensus tracking errors are ensured to be Uniformly Ultimately Bounded. Besides, a minimal inter-sample time is established to avoid the Zeno behavior. Finally, experiments show that the number of controller updates can be reduced to 65.36% by the proposed algorithm.

关键词： multi-missile guidance laws event-triggered mechanism distributed control zero-sum differential games adaptive dynamic programming

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EVENT-TRIGGERED AND SELF-TRIGGERED APPROXIMATE OPTIMAL CONTROL FOR CONSTRAINED-INPUT NONLINEAR SYSTEMS VIA REINFORCEMENT LEARNING

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INTERNATIONAL JOURNAL OF INNOVATIVE COMPUTING INFORMATION AND CONTROL 2025年第3期21卷 769-779页

作者： Liu, Pengda Zhang, Huiyan Ao, Wengang Chongqing Technol & Business Univ Natl Res Base Intelligent Mfg Serv 19 Xuefu Ave Chongqing 400067 Peoples R China Chongqing Innovat Ctr Ind Big Data Co Ltd 11 Tongxing Rd Chongqing 400707 Peoples R China

This paper investigates the event-triggered and self-triggered approximate optimal control issues of nonlinear systems using reinforcement learning approach. First, the optimal control issue with asymmetric input constraints is formulated, via constructing the cost function with nonquadratic utility function. Then, the reinforcement learning method which is implemented by critic neural network is proposed to approximate the optimal control schemes. To further reduce the consumption of computation and communication resources, the dynamic triggering mechanism and self-triggered mechanism are integrated into the adaptive learning framework. Different from the common triggering mechanism, the dynamic triggering mechanism with the preliminary operation is able to reduce the superfluous triggering events when the control precision is achieved. Furthermore, based on the predicted triggering instant, the self-triggered mechanism is designed as an active triggering mechanism instead of the passive one. The stability of the closed-loop system is demonstrated with Lyapunov theorem. In the end, the simulation results validate the effectiveness of the aperiodic triggering adaptive control approach.

关键词： adaptive dynamic programming Reinforcement learning Optimal control Event-triggered control Self-triggered control

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